# Holographic generative flows with AdS/CFT

arXiv: https://arxiv.org/abs/2601.22033 · HTML: https://mlsanity.com/paper/2601.22033/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)
- [Generative Modeling with Phase Stochastic Bridges](https://mlsanity.com/paper/2310.07805/) (2023)
- [GenPhys: From Physical Processes to Generative Models](https://mlsanity.com/paper/2304.02637/) (2023)
- [Renormalizing Diffusion Models](https://mlsanity.com/paper/2308.12355/) (2023)
- [Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points](https://mlsanity.com/paper/2508.04351/) (2025)
- [AdS-GNN -- a Conformally Equivariant Graph Neural Network](https://mlsanity.com/paper/2505.12880/) (2025)

## Abstract (arXiv)

Holography, in the form of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, offers a natural setting for generative modelling. Data on a boundary manifold lifts into a higher-dimensional bulk through a propagator, and this extra dimension plays the role of a flow parameter. We exploit this structure to build GenAdS, an approach to generative flow matching in which the dynamics are represented by the evolution of fields in AdS, together with a residual correction learned by a neural network. Boundary samples are encoded as scalar sources, transported into the bulk along the flow, and decoded after numerical integration. Our paradigm combines a Fourier-space encoding scheme for the data as AdS sources, a normalised radial phase space in which to stage the flow-matching dynamics, and a Klein--Gordon backbone to guide the flow. On a two-dimensional checkerboard benchmark, our experiments show that most of the benefit of GenAdS comes from the Fourier representation and convolutional architecture. However, when we remove momentum-channel regularisation, our most physics-informed GenAdS variant rivals the strongest physics-free control on boundary violation. On MNIST, GenAdS models remain close to a convolutional baseline on fidelity while achieving significantly higher recall at comparable precision, suggesting a fidelity-coverage trade-off. Our findings establish GenAdS as a physically interpretable and experimentally controllable framework for generative modelling, with many avenues for future extension.